Transpose
What do you get when you switch the rows and columns of a matrix?
It's Transpose!
What condition must be true for two matrices A and B to be multiplied?
The Column of A=Rows of B
What matrix times its inverse gives the identity matrix?
The original matrix itself (A × A⁻¹ = I).
What’s the result of (AB)T?
BTAT
If A=
[1 3]
[2 4], what happens if you multiply it with its transpose?
Identity Matrix
Find AT if A=
[1 3]
[2 4]
[1 2]
[3 4]
Multiply
[1 2] * [2 0]
[3 4] [1 2]
[4 4]
[10 8]
Find the determinant of A=
[1 2]
[3 4]
det(A)=(1x4)-(2x3)=-2
True or False: (AB)−1=A−1B−1
False
Find AB if A and B are
[2 1] [1 4]
[0 3] and [2 5] respectively.
[4 13]
[6 15]
If A is
[5 -1 0]
[2 3 4]
Find AT
[5 2]
[-1 3]
[0 4]
If A is 3×2 and B is 2×4, what’s the order of AB?
3x4
Find A-1 for A=
[1 2]
[3 4]
=-1/2 [4 -2]
[-3 1]
=[-2 1]
[1.5 -0.5]
If A=
[2 0]
[1 3] , find (AT)−1
[1 0]
[-1/3 1/3]
Multiply
[1 0] * [2 -1 3]
[-2 3] [0 4 5]
[4 -1]
[2 -1 3]
[-4 14 9]
[8 -8 7]
True or False:
(AT)T=A
True
True or False: AB=BA for all square matrices.
False
True or False: Only square matrices have inverses.
True
If a 2×2 matrix has determinant 0, what can you say about its inverse?
It does not exist.
Multiply
[1 2 3] * [7 8]
[4 5 6] [9 10]
[11 12]
[58 64]
[139 154]
For a 2×3 matrix A, what is the order (size) of AT?
3x2
Multiply:
[1 -1 2] * [2 0]
[0 3 1] [1 4]
[3 5]
[7 6]
[6 17]
Find A-1 for A=
[2 1]
[5 3]
det(A)=1
A-1=
[3 -1]
[-5 2]
If A=
[1 3]
[2 4] , verify AA-1=I
Yes.
Find AB and BA if A and B are
[3 2] & [2 0]
[1 4] [1 3]. Are they equal?
[8 6] [4 6]
[6 12] and [5 12]
NOT EQUAL